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Journal ArticleDOI

A graph-aided method for planning two-level experiments when certain interactions are important

01 May 1992-Technometrics (Taylor & Francis Group)-Vol. 34, Iss: 2, pp 162-175
TL;DR: In this paper, a graph-aided method is proposed to solve the problem of fractional factorial factorial experiment planning, where prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects.
Abstract: In planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects. In this article, we propose a graph-aided method to solve this problem for two-level experiments. First, we choose the defining relations for a 2 n–k design according to a goodness criterion such as the minimum aberration criterion. Then we construct all of the nonisomorphic graphs that represent the solutions to the problem of simultaneous estimation of main effects and two-factor interactions for the given defining relations. In each graph a vertex represents a factor and an edge represents the interaction between the two factors. For the experiment planner, the job is simple: Draw a graph representing the specified interactions and compare it with the list of graphs obtained previously. Our approach is a substantial improvement over Taguchi's linear graphs.
Citations
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Journal ArticleDOI
TL;DR: The individual generalized word length pattern (iGWLP) is proposed, a criterion for choosing best designs when the focus is on a small set of important factors, for which the aliasing of effects involving these factors is minimized.
Abstract: While literature on constructing efficient experimental designs has been plentiful, how best to incorporate prior information when assigning factors to the columns of a nonregular design has receiv...

6 citations


Cites background from "A graph-aided method for planning t..."

  • ...Following Wu and Chen (1992) and Tang (2006), all 2fi’s involving column 1 are said to be clear....

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Dissertation
11 Aug 2011
TL;DR: In this article, the authors introduce the concept of partially clear interactions which leads to a richer class of robust designs when specific interactions are known to be negligible a priori, and develop several methods to construct designs that allow for additional factors to be studied in comparison to designs with clear two-factor interactions.
Abstract: Fractional factorial designs are used in a wide variety of disciplines as a means of studying how changes in the settings of a set of factors influence a response variable. Two important considerations in choosing a fractional factorial design are identifying which effects can be jointly estimated and how the effects not estimated influence the estimation. Orthogonal arrays with clear two-factor interactions provide a class of designs robust to nonnegligible effects. In the first part of this thesis, we introduce the concept of partially clear interactions which leads to a richer class of robust designs when specific interactions are known to be negligible a priori. We develop several methods to construct designs that allow for additional factors to be studied in comparison to designs with clear two-factor interactions. When used in conjunction with non-regular designs, the results become even more powerful as they provide additional flexibility and retain the robust properties. In some situations, the experimenter would like to study factors at more than two levels, such as when curvature has the potential to occur within the experimental region. The second part of this thesis focuses on the estimation of main effects and specified interactions for designs with more than two levels. As designs with more than two levels have additional complications, results are provided that aid in the search for efficient designs that also have robust properties. For two-level designs, the criteria of $G$ and G2-aberration are based on Jcharacteristics and they provide measures of the projection properties of a design. For multilevel designs, extension to G2 was previously done without the use of J-characteristics.

6 citations


Cites background from "A graph-aided method for planning t..."

  • ...Wu and Chen (1992) defined clear two-factor interactions as those which are orthogonal to all main effects and other two-factor interactions....

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  • ...2 (2, 4, 7, 8, 16, 25, 32) (1, 42, 53) 6 10 10-4....

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  • ...Clear 2fi’s were introduced by Wu and Chen (1992) and their existence was examined by Chen and Hedayat (1998)....

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  • ...20 (13, 16, 32, 53) (1, 2, 4, 7, 8, 11, 19) 3 17 17-11....

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01 Jan 2007
TL;DR: Design of Experiments (DoE) contains techniques, such as factorial designs, that help experimenters maximize the information output from conducted experiments and minimize the amount of experimenta.
Abstract: Design of Experiments (DoE) contains techniques, such as factorial designs, that help experimenters maximize the information output from conducted experiments and minimize the amount of experimenta ...

5 citations

Journal ArticleDOI
TL;DR: In this article, the authors propose a new criterion that is defined on a column of the design matrix to measure the aliasing of the effect assigned to this column and effects involving other factors.

5 citations

References
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Book
01 Jan 1978

5,151 citations

Book
01 Jan 2015
TL;DR: This book offers a complete blueprint for structuring projects to achieve rapid completion with high engineering productivity during the research and development phase to ensure that high quality products can be made quickly and at the lowest possible cost.
Abstract: From the Publisher: Phadke was trained in robust design techniques by Genichi Taguchi, the mastermind behind Japanese quality manufacturing technologies and the father of Japanese quality control. Taguchi's approach is currently under consideration to be adopted as a student protocol with the US govrnment. The foreword is written by Taguchi. This book offers a complete blueprint for structuring projects to achieve rapid completion with high engineering productivity during the research and development phase to ensure that high quality products can be made quickly and at the lowest possible cost. Some topics covered are: orthogonol arrays, how to construct orthogonal arrays, computer-aided robutst design techniques, dynamic systems design methods, and more.

3,928 citations


"A graph-aided method for planning t..." refers methods in this paper

  • ...For a review on efficient algorithms for testing graph isomorphism, see Read and Corneil (1977) and Hoffman (1982)....

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  • ...For simplicity we do not include in this article the column numbers for the lines, which can be easily read from the interaction tables given by Phadke (1989) and Taguchi (1987)....

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Journal ArticleDOI
TL;DR: The present state of the art of isomorphism testing is surveyed, its relationship to NP-completeness is discussed, and some of the difficulties inherent in this particularly elusive and challenging problem are indicated.
Abstract: The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.

519 citations

Journal ArticleDOI
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.

420 citations

01 Jan 1980
TL;DR: The concept of resolution was introduced by Box and Hunter as discussed by the authors, who defined the resolution of a two-level fractional factorial design as the length of the shortest word in the defining relation.
Abstract: Fractional factorial designs-especially the twolevel designs-are useful in a variety of experimental situations, for example, (i) screening studies in which only a subset of the variables is expected to be important, (ii) research investigations in which certain interactions are expected to be negligible and (iii) experimental programs in which groups of runs are to be performed sequentially, ambiguities being resolved as the investigation evolves (see Box, Hunter and Hunter, 1978). The literature on fractional factorial designs is extensive. For references before 1969, see the comprehensive bibliography of Herzberg and Cox (1969). For more recent references, see Daniel (1976) and Joiner (1975-79). A useful concept associated with 2k-P fractional factorial designs is that of resolution (Box and Hunter, 1961). A design is of resolution R if no cfactor effect is confounded with any other effect containing less than R c factors. For example, a design of resolution III does not confound main effects with one another but does confound main effects with two-factor interactions, and a design of resolution IV does not confound main effects with two-factor interactions but does confound two-factor interactions with one another. The resolution of a two-level fractional factorial design is the length of the shortest word in the defining relation. Usually an experimenter will prefer to use a design which has the highest

354 citations